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Application Note AN 

Current Feedback 

November 1 992 

The use of clever circuit arcliitectures and tlie deveiopment of fiigli-speed 
complementary BJT processes make it possible to achieve monolithic 
speeds and bandwidths hitherto available only in hybrid form. 

— Sergio Franco, San Francisco State University 
1600 Holloway Avenue, San Francisco, CA 94132 

In their effort to approximate the ideal op amp, manufac- 
turers must not only maximize the open-loop gain and 
minimize input-referred errors such as offset voltage, bias 
current, and noise, but must also ensure adequate band- 
width and settling-time characteristics. Amplifier dynamics 
are particuularly important in applications like high- 
speed DAC buffers, subranging ADCs, S/H circuits, ATE 
pin drivers, and video and IF drivers.^ 

Being basically voltage-processing devices, op amps 
are subject to the speed limitations inherent to voltage- 
mode operation, stemming primarily from the stray cap- 
acitances of nodes and the cutoff frequencies of transis- 
tors. Particularly severe is the effect of the stray capac- 
itances between the input and output nodes of high-gain 
inverting stages because of the Miller effect which mul- 
tiplies the stray capacitance by the voltage gain of the 

On the other hand, it has long been recognized that 
current manipulation is inherently faster than voltage 
manipulation. The effect of stray inductances in a circuit 
is usually less severe than that of its stray capacitances, 
and BJTs can switch currents much more rapidly than 
voltages. These technological reasons form the basis of 
emitter-coupled logic, bipolar DACs, current conveyors, 
and the high-speed amplifier topology known as current- 

Fortruecurrent-modeoperation, all nodes in the circuit 
should ideally be kept at fixed voltages to avoid the slow- 
down effect by their stray capacitances. However, since 
the output of the amplifier must be a voltage, some form 
of high-speed voltage-mode operation must also be 
provided at some point. This is achieved by employing 
gain configurations that are inherently immune from the 
Miller effect, such as the common-collector and the 
cascode configurations, and by driving the nodes with 
push-pull stages to rapidly charge/discharge their stray 

To ensure symmetric rise and fall times, the npn and 
pnp transistors must have comparable characteristics in 
terms of cutoff frequency ft. Traditionally, monolithic pnp's 
have been plagued by much poorer performance char- 
acteristics than their npn counterparts. However, the 
recent development of truly complementary high-speed 
processes makes it possible to achieve monolithic speeds 
that were hitherto available only in hybrid form. 

The advantages of the current-feedback topology are 
best appreciated by comparing it against that of the 
conventional op amp.^" 

The Conventional Op Amp 

The conventional op amp consists of a high input- 
impedance differential stage followed by additional gain 
stages, the last of which is a low output-impedance stage. 
As shown in the circuit model of Fig. la, the op amp 
transfer characteristic is 

Vo = a(jf)Vd (1) 

where Vo is the output voltage; Vd = Vp — Vn is the 
differential input voltage; and a(jf), a complex function of 
frequency f, is the open-loop gain. 

Connecting an external network as in Fig. lb creates 
a feedback path along which a signal in the form of a 
voltage is derived from the output and applied to the 
noninverting input. By inspection. 




Ri + R2 





Fig. 1 : Circuit model of thie conventionai op amp, and connec- 
tion as a noninverting amplifier. 

Substituting into Eq. (1), collecting, and solving for the 
ratio Vo/ Vi yields the familiar noninverting amplifier transfer 



1 + 

R2 1 


1 + 1/T(if) 


where A(jf) represents the closed-loop gain, and 


1 + R2/R1 


represents the loop gain. 

© 1992 National Semiconductor Corporation 
Printed in ttie U.S.A. 

The designation loop gain stems from the fact that if we 
break the loop as in Fig. 2a and inject a test signal Vx with 
Vi suppressed, the circuit will first attenuate Vx to produce 
Vn = Vx/(1 + R2/R1), and then amplify Vn to produce 
Vo = — aVn. Hence, the gain experienced by a signal in 
going around the loop is Vo/Vx = — a/(1 + R2/R1). The 
negaf/Veof this ratio represents the loop gain, T^ —(Vo/Vx). 
Hence, Eq. (4). 

The loop gain gives a measure of how close A is to the 
ideal value 1 + R2/R1, also called the noise gain of the 
circuit. By Eq. (3), the larger T, the better. To ensure 
substantial loop gain over a wide range of closed-loop 
gains, op amp manufacturers strive to make a as large as 
possible. Consequently, Vd will assume extremely small 
values since Vd = Vo/a. In the limit a ^ °° we obtain Vd -* 0, 
that is, Vn -^ Vp. This forms the basis of the familiar op amp 
rule: when operated with negative feedback, an op amp 
will provide whatever output voltage and current are 
needed to ideally force Vn to follow Vp. 



Fig. 2: Test circuit to find the ioop gain, and graphical method 
to determine the ciosed-ioop bandwidth f^. 

Gain-Bandwidth Tradeoff 

Large open-loop gains can physically be realized only 
over a limited frequency range. Past this range, gain rolls 
off with frequency. Most op amps are designed for a 
constant rolloff of — 20dB/dec, so that the open-loop 
response can be expressed as 





where ao represents the dc gain, and fa is the — 3dB 
frequency of the open-loop response. Both parameters 
can be found from the data sheets. For example, the 741 
op amp has ao — 2 X 10= and U — 5Hz. 

Substituting Eq. (5) into Eq. (4) and then into Eq. (3), and 
exploiting the fact that (1 + R2/Ri)ao<1, we obtain 











fA = 







represents the closed-loop bandwidth, and ft = aofa 
represents the open-loop unity-gain frequency, that is 
the frequency at which | a | = 1. For instance, the 741 
op amp has f, = 2 X 10^ X 5 = 1 MHz. 

Equation (7) reveals a gain-bandwidth tradeoff. As we 
raise the R2/R1 ratio to increase the closed-loop gain, we 
also decrease its bandwidth in the process. Moreover, by 
Eq. (4), the loop-gain is also decreased, thus leading to a 
greater closed-loop gain error. 

The above concepts can also be visualized graphically. 
Since Eq. (4) implies | T |dB = 20 log | T | = 20 log | a | 
- 20 log (1 + R2/R1) = I a IdB - (1 + R2/Ri)dB, it fol- 
lows that the loop gain can be found graphically as the 
difference between the open-loop gain and the noise 
gain. This is shown in Fig. 2b. The frequency at which 
the two curves meet is called the crossover frequency. 
At this frequency we have T = 1 /— 90° = — j, that is, 
I A I = (1 -I- R2/R1) / \/2. Thus, the crossover frequency 
represents the — 3dB frequency of the closed-loop re- 
sponse, that is, the closed-loop bandwidth fA. 

We now see that increasing the closed-loop gain shifts 
the noise-gain curve upward, thus reducing the loop 
gain, and causes the crosspoint to move up the | a | 
curve, thus decreasing the closed-loop bandwidth. 
Clearly, the circuit with the widest bandwidth and the 
highest loop gain is also the one with the lowest closed- 
loop gain. This is the voltage follower, for which R2/ Ri = 0, 
so that A = 1 and fA = ft- 

Slew- Rate Limiting 

To fully characterize the dynamic behavior of an op amp, 
we also need to know its transient response. If an op amp 
with the response of Eq. (5) is operated as a unity-gain 
voltage follower and is subjected to a suitably small 
voltage step, its dynamic behavior will be similar to that 
of an RC network. Applying an input step AV will cause 
the output to undergo an exponential transition with 
magnitude AVo = AV, and with a time-constant 
T = 1/{277-ft). For the 741 op amp we have 
r = 1/(27rX 106) = 170 ns. 

The rate at which the output changes with time is 
highest at the beginning of the exponential transition, 
when its value is AVo/r. Increasing the step magnitude 
increases this initial rate of change, until the latter will 
saturate at a value called the slew-rate (SR). This effect 
stems from the limited ability of the internal circuitry to 
charge/discharge capacitive loads, especially the com- 
pensation capacitor responsible for open-loop 
bandwidth fa. 

To illustrate, refer to the circuit model of Fig. 3, which 
is typical of many op amps." The input stage is a trans- 
conductance block consisting of differential pair Qi— Q2 
and current mirror Q3— Q4. The remaining stages are 
lumped together as an integrator block consisting 
of an inverting amplifier and the compensation capa- 
citor C. Slew-rate limiting occurs when the trans- 
conductance stage is driven into saturation, so that all the 
current available to charge/discharge C is the bias 
current / of this stage. For example, the 741 op amp has 
\ = 20fjA and C = 30 pF, so that SR = l/C = 0.67 VZ/ys. 
The step magnitude corresponding to the onset of 
slew-rate limiting is such that AV/r = SR, that is, 
AV = SR X r = (0.67 V//ys) X (1 70 ns) = 1 1 6 mV As long 
as the step is less than 116 mV, a 741 voltage follower will 
respond with an exponential transition governed by 
r== 1 70 ns, whereas for a greater input step the output will 
slew at a constant rate of 0.67 V///s. 


Fig. 3: Simplified slew-rate model of a conventional op amp. 

In many applications tlie dynamic parameter of greatest 
concern is the settling time, that is, the time it takes for 
the output to settle and remain within a specified band 
around its final value, usually for a full-scale output 
transition. Clearly, slew-rate limiting plays an important 
role in the settling-time characteristic of the device. 

The Current-Feedback Amplifier 

As shown in the circuit model of Fig. 4, the architecture 
of the current-feedback amplifier (CF amp) differs from 
the conventional op amp In two respects:^ 

1. The Input stage is a unity-gain voitage buffer con- 
nected across the Inputs of the op amp. Its function 
Is to force Vn to follow Vp, very much like a conven- 
tional op amp does via negative feedback. However, 
because of the low output impedance of this buffer, 
current can easily flow in or out of the inverting input, 
though we shall see that in normal operation this 
current Is extremely small. 



Fig. 4: Circuit model of the current-feedback amplifier, and 
connection as a noninverting amplifier. 

2. Amplification is provided by a transimpedance 
amplifier which senses the current delivered by the 
buffer to the external feedback network, and pro- 
duces an output voltage Vo such that 

Vo = Z(jf)ln 


where z(jf) represents the transimpedance gain of 
the amplifier, in V/A or Q, and In is the current out 
of the inverting input. 

To fully appreciate the inner workings of the CF amp, 
it is instructive to examine the simplified circuit diagram 
of Fig. 5a. The input buffer consists of transistors Qi 
through Q4. While Qi and Q2 form a low output-Impedance 
push-pull stage, Q3 and Q4 provide Vbe compensation for 
the push-pull pair, as well as a Darlington function to raise 
the input impedance. 

Summing currents at the inverting node yields 
h — I2 = In, where I1 and I2 are the push-pull transistor 

currents. Two Wilson current mirrors, consisting of tran- 
sistors Qg— Q10— Q11 and Q13— Q14— Q15, reflect these 
currents and recombine them at a common node, whose 
equivalent capacitance to ground has been designated 
as C. By mirror action, the current through this capacitance 
is Ic = h ~ I2, that is 




The voltage developed by C In response to this current 
is then conveyed to the output via a second buffer, 
consisting of Q5 through Qs. The salient features of the CF 
amp are summarized in block diagram form in Fig. 5b. 

When the amplifier loop is closed as in Fig. 4b, and 
whenever an external signal tries to imbalance the two 
inputs, the input buffer will begin sourcing (or sinking) an 
imbalance current L to the external resistances. This 
imbalance is then conveyed by the Wilson mirrors to 
capacitor C, causing Vo to swing in the positive (or 
negative) direction until the original imbalance In is 
neutralized via the negative feedback loop. Thus, In plays 
the role of error signal in the system. 

Fig. 5: Simplified circuit diagram and block diagram of a 
current-feedback amplifier. 

To obtain the closed-loop transfer characteristic, refer 
again to Fig. 4b. Summing currents at the inverting node 


Vo - Vn 


since the buffer ensures Vn = Vp = Vi we can rewrite as 


Ri II R2 



confirming that the feedback signal V0/R2 is now in the 
form of a current Substituting into Eq. (8), collecting, and 
solving for the ratio Vo/V, yields 







where A(jf) represents the c/osed-/oop gain of the circuit, 




represents the loop gain. This designation stems again 
from the fact that if we break the loop as in Fig. 6a, 
and inject a test voltage Vx with the input V suppressed, 
the circuit will first convert Vx to the current \„ = — Vx/R2, 
and then convert In to the voltage Vo = zin, so that 
T = — (Vo/Vx) = Z/R2, as expected. 

In an effort to ensure substantial loop gain to reduce the 
closed-loop gain error, manufacturers strive to make zas 
large as possible relative to the expected values of R2. 
Consequently, since L = Vo/z, the inverting-input current 
will be very small, though this input is a low-impedance 
node because of the buffer. In the limit z ^ 0° we obtain 
In -^ 0, indicating that a CF amp will provide whatever 
output voltage and current are needed to ideally drive In 
to zero. Thus, the conventional op amp conditions Vn = Vp 
and In = Ip = hold for CF amps as well. 




Fig. 6: Test circuit to find the loop gain, and graphical method 
to determine the ciosed-loop bandwidth f^. 

No Gain-Bandwidth Tradeoff 

The transimpedance gain of a practical CF amp rolls off 
with frequency according to 


1 + j(f/fa 


where Zo is the dc value of the transimpedance gain, and 
fa is the frequency at which rolloff begins. For instance, 
from the data sheets of the CLC401 CF amp (Corn- 
linear Co.) we find Zo = 710 kQ, and fa = 350 kHz. 

Substituting Eq. (14) into Eq, (13) and then into Eq. (12), 
and exploiting the fact that R2/Z0 < 1, we obtain 









represents the closed-loop bandwidth, for R2 in the kQ 
range, fA is typically in the 100 MHz. Retracing previous 
reasoning, we see that the noise-gain curve is now R2, 
and that fA can be found graphically as the frequency at 
which this curve meets the | z | curve, see Fig. 6b. 

Comparing with Eqs. (6) and (7), we note that the 
closed-loop gain expressions are formally identical. 
However, the bandwidth now depends only on R2 rather 
than on the closed-loop gain 1 + R2/R1. Consequently, 
we can use R2 to select the bandwidth, and Ri to select 
the gain. The ability to control gain independently of 
bandwidth constitutes a major advantage of CF amps 
over conventional op amps, especially in automatic gain 
control applications. This important difference is high- 
lighted in Fig. 7. 

1 Gain 

( , Coin 






Fig. 7: Comparing the gain-bandwidth relationship of conven- 
tional op amps and current-feedback amplifiers. 

Absence of Slew-Rate Limiting 

The other major advantage of CF amps is the inherent 
absence of slew-rate limiting. This stems from the fact 
that the current available to charge the internal capaci- 
tance at the onset of a step is proportional to the step 
regardless of its size. Indeed, applying a step AV induces, 
by Eq. (11), an initial currentimbalanceln = AVi/(Ri || R2), 
which the Wilson mirrors then convey to the capacitor. 
The initial rate of charge is, therefore, Ic/C = L/C = 
AV/[(Ri||R2)C] = [AVi(1+R2/Ri)]/(R2C) = AVo/(R2C), 
indicating an exponential output transition with time- 
constant T = R2C. Like the frequency response, the 
transient response is governed by R2 alone, regardless of 
the closed-loop gain. With R2 in the kQ range and C in 
the pF range, r comes out in the ns range. 

The rise time is defined as the amount of time tr it takes 
for the output to swing from 10% to 90% of the step size. 
For an exponential transition, tr = r X In (0.9/0.1) = 2.2t. 

For example, the CLC401 has tr = 2.5 ns for a 2V output 
step, indicating an effective r of 1 .1 4 ns. The time It takes 
for the output to settle within 0.1% of the final value is 
ts = T In 1 000 ^ It. For the CLC401 , this yields ts - 8 ns, 
in reasonable agreement with the data sheet value 
of 10 ns. 

The absence of slew-rate limiting not only allows for 
faster settling times, but also eliminates slew-rate related 
nonlinearities such as intermodulation distortion. This 
makes CF amps attractive in high-quality audio amplifier 

Second-Order Effects 

The above analysis indicates that once R2 has been set, 
the dynamics of the amplifier are unaffected by the 
closed-loop gain setting. In practice it is found that 
bandwidth and rise time do vary with gain somewhat, 
though not as drastically as with conventional op amps. 
The main cause is the non-zero output impedance of the 
input buffer, whose effect is to alter the loop gain and, 
hence, the closed-loop dynamics. 

Referring to Fig. 8a and denoting this impedance as Ro, 
we note that the circuit first converts V, to a current 
Ir2 = Vx/ (R2 + Ri II Ro), then it divides Irs to produce 
In = Ir2Ri/(Ri + Ro), and finally it converts In to the 
voltage Vo = zip. Eliminating Ipg and L and letting 
T = -Vq/Vx yields T = Z/Z2, where 

Z2 — R2 

1 + 




Thus, the effect of Ro is to increase the noise gain from 
R2 to R2[ 1 + Ro/ (Ri IIR2)], see Fig. 8b, curve 1. Conse- 
quently, both bandwidth and rise time will be reduced by 
a proportional amount. 



Fig. 8: Test circuit to investigate the effect of Rq, and noise- 
gain curves for tlie case of: (1) purely resistive feedbacic, (2) a 
capacitance in paraiiel witii Rj, and (3) the same capacitance 
in parallel with R^. 

Replacing R2 with Z2 in Eq. (16) yields, after simple 


1 -h 


1 -h 

R2 \ 


where ft = zofa/R2 represents the extrapolated value of 
f A in the limit Ro ^ 0. This equation indicates that bandwidth 
reduction due to Ro will be more pronounced at high 
closed-loop gains. As an example, suppose a CF amp has 

Ro = 50Q, R2 = 1.5 kQ, and ft = 100 MHz, so that 
fA = 108/[1 -I- (50/1500)Ao] = 108/(1 + Ao/30), where 
Ao = 1 + R2/R1. Then, the bandwidths corresponding to 
Ac = 1, 10, and 100 are, respectively, fi = 96.8 MHz, 
fio = 75.0 MHz, and fioo = 23.1 MHz. Note that these 
values still compare favorably with a conventional op amp, 
whose bandwidth would be reduced, respectively, by 1, 
10, and 100. 

If so desired, the external resistance values can be 
predistorted to compensate for the bandwidth reduction 
at high gains. Turning Eq. (18) around yields the required 
value of R2 for a given laandwidth fA and gain Ao. 




while the required value of Ri for the given gain Aq is 



Ao - 1 


As an example, suppose we want the above amplifier to 
retain its 100 MHz bandwidth at a closed-loop gain of 10. 
Since with R2 = 1 .5 kQ this device has Zofa/R2 = 1 00 MHz, 
it follows that zofa = 1 0^ X 1 500 = 1 .5 X 1 0" Q X Hz. Then, 
the above equations yield R2 = 1.5 X lO^VIOs - 50 X 10 
= 1 kn, and Ri = 1000/(10- 1) = 111 Q. 

Besides the dominant pole at fa, the open-loop response 
of a practical amplifier presents additional poles above 
the crossover frequency. As shown in Fig. 8b, the effect 
of these poles is to cause a steeper gain rolloff at this 
frequency, further reducing the closed-loop bandwidth. 
Moreover, the additional phase-shift due to these poles 
decreases the phase margin somewhat, thus causing a 
small amount of peaking in the frequency response, and 
ringing in the transient response. 

Finally, it must be said that the rise time of a practical 
CF amp does increase with the step size somewhat, due 
primarily to transistor current gain degradation at high 
current levels. For instance, the rise time of the CLC401 
changes from 2.5 ns to 5 ns as the step size is changed 
from 2\/ to 5V. In spite of second-order limitations, CF amps 
still provide superior dynamics. 

CF Applications Considerations 

Although the above treatment has focused on the non- 
inverting configuration, the CF amp will work as well in 
most other resistive feedback configurations, such as the 
inverting amplifier, the summing and differencing amplifier, 
l-V and V-l converters, and KRC active filters." In fact, the 
derivation of the transfer characteristic of any of these 
circuits proceeds along the same lines as conventional 
op amps. Special consideration, however, require the 
cases in which the feedback network includes reactive 
elements, either intentional or parasitic. 

Consider first the effect of a feedback capacitance 
C2 in parallel with R2 in the basic circuit of Fig. 8a. 
Letting Z = R2ll(1/sC2), the noise gain becomes 
Z2 = Z[1 + Ro/(Ri||Z)]. After expanding, it is readily 
seen that the noise-gain curve has a pole at fp = 1 / 
(277-R2C2) and a zero at fz = 1/[277-(Ro||Ri ||R2)C2], as 
shown in Fig. 8b, curve 2. Consequently, the crossover 
frequency will be pushed into the region of substantial 

phase shift due to the higher-order poles of z. If the 
overall shift reaches —180° at this frequency, then 
T = 1 /— 180° = —1 there, indicating that A will become 
infinite by Eq. (12), and the circuit will oscillate. Even if the 
phase shift fails to reach — 180°, the closed-loop response 
may still exhibit intolerable peaking and ringing. Hence, 
capacitive feedback must be avoided with CF amps. To 
minimize the effect of stray feedback capacitances, man- 
ufacturers often provide Rz internally. 

CF Integrators 

To synthesize the integrator function in CF form, which 
provides the basis for dual-integrator-loop filters and 
oscillators as well as other popular circuits, we must use 
configurations that avoid a direct capacitance between 
the output and the inverting input. One possibility is 
offered by the Deboo integrator," which belongs to the 
class of KRC filters and is therefore amenable to CF 
realization. Its drawback is the need for tightly matched 
resistances, if lossless integration is desired. The alterna- 
tive of Fig. 9 not only meets the given constraint, but also 
provides active compensation, a highly desirable feature 
to cope with Q-enhancement problems in dual-integrator- 
loop filters." Using standard op amp analysis techniques, 
it is readily seen that the unity-gain frequency of this 
integrator is fo - (R2/Ri)/(27rRC). 

reasoning," it is easily seen that f a = [zofafz/ (Ro + F!2) ] ^ '^, 
where fz = 1/[27r(Ro|| R2)Ci]. Imposing fp = fA yields 






(a) (b) 

Fig. 10: DAC output capacitance compensation. 

To cope with impractically low values of C2, it is con- 
venient to drive C2 with a voltage divider as in Fig. 10b, 
since this will scale the value of C2 to the more practical 

1 + 

Rb ^ 


It can be shown that for this technique to be effective we 
must choose Rb < R2. As an example, suppose a DAC 
having Ci = 1 00 pF feeds the CF amp considered earlier. 
Then, Eq. (21) yields C2 = [50 X 100 X 10"'^/ (27?- X 1.5 
X 103 X 1.5 X 10ii)]i''2 = 1.88 pF To scale it to a more 
practical value, use ^ Ra = 500 and Rb = 5000. Then, 
Cc = (1 +500/50) 1.88=: 21 pF This estimate may require 
some fine tuning to optimize the transient response. 

Additional useful application hints can be found in 
Ref. [5]. 

Fig. 9: Activeiy-compensated CF integrator. 

Stray Input-Capacitance Compensation 

Next, consider the effect of an input capacitance Ci in 
parallel with Ri in the basic circuit of Fig. 8a. Letting 
Z = Ri||(1/sCi), the noise gain is now Z2 = R2[1 + 
Ro/(Z||R2)]. After expanding, it is readily seen that 
the noise-gain curve has a zero at fz = 1/[27r 
(Roll Ri II R2)Ci], as shown in Fig. 8b, curve 3. If Ci is 
sufficiently large, the phase of Tat the crossover frequency 
will again approach —180°, bringing the circuit on the 
verge of instability. This is of particular concern in current- 
mode DAC output buffering, where Ci is the output 
capacitance of the DAC, typically in the range of a few 
tens to a few hundreds of picofarads, depending on the 
DAC type. 

Like a conventional op amp, the CF amp can be 
stabilized by using a feedback capacitance C2 to introduce 
sufficient phase-lead to compensate for the phase-lag 
due to the input capacitance Ci. For a phase margin of 
45°, choose the value of C2 so that the noise-gain pole 
fp = 1 / (277-R2C2) coincides with the crossover frequency 
fA, as shown in Fig. 10a. Using asymptotic Bode-plot 


1. P. Harold, Current-Feedbacl< Op Amps Ease High- 
Speed Circuit Design, to be published in EDN, 1988. 

2. A New Approach to Op Amp Design, Comlinear Cor- 
poration Application Note 300-1, March 1985. 

3. 1988 Current-Feedbacl< Seminar, Comlinear Corp. 

4. Sergio Franco, Design with Operational Amplifiers and 
Analog ICs, McGraw-Hill Book Company, 1988. 

5. Current-Feedback Op Amp Applications Circuit Guide, 
Comlinear Corporation Application Note OA-07, 1 988. 

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